SOLUTION: I cannot solve this: I can use: Transportation, Material Implication, Material Equivalence, Exportation, Tautology, Double Negation, Commutation, Association, Distribution, Demorga

Question 188933: I cannot solve this: I can use: Transportation, Material Implication, Material Equivalence, Exportation, Tautology, Double Negation, Commutation, Association, Distribution, Demorgan's Theorem, Modus Ponems, Modus Tollens, Hypothetical Syllogism, Conjunstion, Simplification, Addition, Constructive Dilemma, Absorption and Disjuntive Syllogism.
1. p -> (q & r)
2. ~t -> (~r v ~s) Therefore: (p & s) -> t

I know that you must somehow get:
~p
~p v ~s Add
~(p & s) Demorgans
~(p & s) v t Addition
(p & s) -> t Implication OR
~t -> t
t v t Implication
t Tautology
t v ~(p & s) Addition
~(p & s) v t Commutation
(p & s) -> t Implication
But I cannot get the steps before these. Please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Note: try to involve every premise (the given lines) to find the conclusion.


1. p -> (q & r)
2. ~t -> (~r v ~s) Therefore: (p & s) -> t 
----------------------------------------------
3.  ~~t v (~r v ~s)                          2     Material Implication
4.  t v (~r v ~s)                            3     Double Negation
5.  (~r v ~s) v t                            4     Commutation
6.  ~r v (~s v t)                            5     Association
7.  ~r v (s -> t)                            6     Material Implication
8.  r -> (s -> t)                            7     Material Implication
9. ~p v (q & r)                              1     Material Implication
10. (~p v q) & (~p v r)                      9     Distribution
11. (~p v r) & (~p v q)                      10    Commutation
12. ~p v r                                   11    Simplification
13. p -> r                                   12    Material Implication
14. p -> (s -> t)                            13,8  Hypothetical Syllogism
15. (p & s) -> t                             14    Exportation

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